Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22577301 | C2 | semidirect |
| 4. #22577274 | C2 | semidirect |
| 5. #22577269 | C2 | semidirect |
| 6. #22577262 | C2 | semidirect |
| 7. #95×D137 | C2 | semidirect |
| 8. C4×C4⋊C4×C137 | C2 | semidirect |
| 13. C4×D548 | C4 | semidirect |
| 37. C2×C4×D137 | C2×C4 | semidirect |
| 39. C4⋊Dic137 | C2×C4 | semidirect |
| 42. #14555487 | C2×C4 | semidirect |
| 50. C42×C137 | C2×C4 | semidirect |
| 56. D548 | C4⋊C4 | semidirect |
| 101. C137 | #2349 | semidirect |
| 109. C4×C4⋊C4 | D137 | semidirect |
| 152. C42 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| #22577301 | 2 |
| #22577274 | 2 |
| #22577269 | 2 |
| #22577262 | 2 |
| #95×D137 | 2 |
| C4×C4⋊C4×C137 | 2 |
| #2349 | 137 |